Clifford Algebraic Remark on the Mandelbrot Set of Two--Component Number Systems

Abstract

We investigate with the help of Clifford algebraic methods the Mandelbrot set over arbitrary two-component number systems. The complex numbers are regarded as operator spinors in D\times spin(2) resp. spin(2). The thereby induced (pseudo) normforms and traces are not the usual ones. A multi quadratic set is obtained in the hyperbolic case contrary to [1]. In the hyperbolic case a breakdown of this simple dynamics takes place.

arXiv commentLaTeX, 27 pages, 6 fig. with psfig included

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